Proceedings of the 45th European Microwave Conference
Scanning Microwave Microscopy for Nanoscale Characterization of Semiconductors: De-embedding reflection contact mode measurements L. Michalas1, A. Lucibello1, G. Badino2, C.H. Joseph1, E. Brinciotti2, F. Kienberger2, E. Proietti1 and R. Marcelli1 1
National Research Council, Institute for Microelectronics and Microsystems (CNR-IMM) Via del Fosso del Cavaliere 100, 00133 Rome, Italy
[email protected] 2
Keysight Technologies Austria GmbH Gruberstrasse 40, 4020, Linz, Austria
[email protected]
both benefit from the very sensitive analysis performed with help of both amplitude and phase response of the network analyzer system. One of the most popular uses attracting intensive research interest in late years is the development of nondestructive techniques for quantitative characterization of semiconductor materials and devices with nanoscale resolution.
Abstract—A methodology towards de-embedding contact mode scanning microwave microscopy (SMM) reflection measurements is presented. A calibration standard that consists of differently doped stripes is required, while the reflection coefficient amplitude │S11│, is modeled and analyzed in the linear scale, instead of the commonly adopted dB scale. This allows the straightforward experimental determination of important parameters such as the effective tip radius and the magnitude of stray capacitances. Values of 145 nm and 22 fF have been obtained respectively. The proposed methodology can be easily and repeatedly performed during the experimental procedure, offering in this way the necessary de-embedding to get an enhanced accuracy on SMM measurements for semiconductors characterization.
SMM resolution is determined by the AFM tip radius and therefore is typically in nanometer scale. However, the accurate determination of the effective scanned area is not a trivial task yet. This is because the effective scanned area that contributes to the microwave signals reflection in general is different with respect to the nominal tip radius. This mainly arises from experimental reasons such as the contribution of fringing fields around the tip end, and also due to tip flattening/wearing during the experimental procedure. In addition, it should also be taken into consideration that, when working at the nanoscale, any deviation from nominal values may have important contributions. A parallel effect to be assessed towards the improvement of SMM accuracy is the presence of parasitic capacitances. These are introduced mainly by the interactions between the boundaries of tip with the experimental environment. Such capacitances can be in the same order of those formed by the tip edge and the sample, therefore their determination is of major importance. Regarding the determination of the above mentioned parameters, a calibration approach introduced by H.P Huber et. al. in [5] is based on SMM measurements on a staircase calibration standard. Recently G. Gramse et al. [6] have introduced a calibration methodology that does not require the use of a calibration sample; the workflow is based on the acquisition of an Electrostatic Force Microscopy (EFM) approach curve.
Keywords—Scanning Microwave Microscopy (SMM); Deembedding; Semiconductors; RF characterization; nanoscale
I. INTRODUCTION Scanning Microwave Microscopy (SMM) is a technique that combines the sensitivity of microwave measurements with the resolution of atomic force microscopy (AFM). In a typical contact-mode SMM reflection experiment, a microwave signal is applied to the device under test (DUT) at a point of contact through a conductive AFM tip. The reflected signal, result of the tip-sample system interaction, is measured with a vector network analyzer (VNA). By using the appropriate experimental setup, to achieve the required match [1] and thus high sensitivity, the reflective signal (S11) is determined by the properties of the DUT in the vicinity of the contact area. Therefore SMM can provide high sensitivity information on the material properties with the resolution of the effective probe edge size, typically in the sub-micrometer or down to nanometer scale. Thus, SMM is a useful tool for the characterization of metallic, semiconducting or insulating samples. It can also be used in non-contact mode, i.e. in near field conditions, depending on the nature of device under test [2,3]. Very recently a transmission mode approach, based on recording the transmitted signal (S21), was also introduced [4]. By means of SMM, imaging and material science issues take
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The present paper aims to introduce a new methodology towards de-embedding reflection and contact mode scanning microwave measurements for semiconductor characterization. A calibration standard that consists of stripes with different doping levels is required. The analysis is based on the linear relation between the magnitude of S11 and the reflective capacitance usually obtained in these cases [5,7,8], but the
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analysis is performed in the linear scale instead of the commonly adopted dB scale, an approach not reported before. The implementation of the linear scale allows a deeper insight into the physics underneath the SMM process and leads to a straightforward experimental estimation of the effective tip radius and of the system stray capacitances. Moreover, using known capacitance values allows determining exactly the quantities to be used for calibration purposes, in a direct way.
other influence that may contribute or may be modeled as parallel capacitance. By replacing term C in Eq. (2) by Eq. (3) it becomes clear that a linear relation is expected to connect the magnitude of S11 measured or transformed in the linear scale to the expected capacitance of the MOS system calculated per unit area as pointed out clearly by Eq. (4)
S11
II. MODELING REFLECTION MODE SMM In contact mode experiments with scanning microwave microscopy, the material or the device under investigation is in direct contact with the SMM tip, and can be quite accurately modeled. This is true especially for thin tips. The system can be modeled as a shunt capacitor properly terminated with a 50 Ω shunt resistance. For a properly terminated shunt capacitor the reflection coefficient for microwaves signals, Γ or S11, is expressed as
RF Z 0 (Reff2 ) 2
CMOS
RF Z 0Cstray 2
(4)
Therefore, by plotting the experimental results obtained on the calibration standard as a function of the expected capacitance and by the application of a linear regression process, the slope provides an estimation of the effective scanned area, thus the tip radius, and the intercept provides the parallel contributions of stray capacitances. III. EXPERIMENTAL
S11
jRF CZ 0 2 jRF CZ 0 (RF CZ 0 ) 2 2 jRF CZ 0 4 (RF CZ 0 ) 2
The SMM experimental setup consists of an Atomic Force Microscope (AFM) interfaced with a Vector Network Analyzer (VNA). A 50 Ω shunt resistor and a resonator are also integrated in the SMM system to match the high impedance of the tip/DUT interface to the impedance of the microwave instrumentation, increasing in this way the sensitivity. In our experimental procedure a Keysight΄s N5230 PNA was matched with a Keysight΄s LS5600 AFM with commercially available platinum tips especially designed for SMM measurements, i.e. Rocky Mountain Nanotechnology 25Pt300A, with a spring constant of 18N/m [10]. Before scanning the sample, the SMM tip is in contact with the DUT, and a VNA frequency sweep is performed from 1 to 20 GHz (i.e. within the frequency interval which is the current state-of-art for the technology of the SMM probes). Multiple frequencies of resonance are obtained by using a resonator integrated with the probe. Then, although the method can be in principle applied at any frequency, the most appropriate one is chosen between those characterized by best imaging and impedance responses for the measurements to be performed.
(1)
where ωRF = 2πfRF with fRF being the RF frequency, whereas C is the capacitance formed by the tip and the DUT, Z0 is the system impendence, 50 Ω in our case, and j2 = -1. With AFM tips having a radius in the nanometer scale the capacitances formed by the tip edge and the DUT, in case of semiconductor characterization, ranges from femto-Farad down to atto-Farad. For such capacitances operated at GHz range of frequencies, as required for SMM assessment, the second order terms in Eq. (1) are expected to have minor contribution with respect to the other terms and therefore the magnitude of S11 can be expressed as
S11
RF CZ 0 2
(2)
For the methodology proposed in this work a calibration standard is required. For this purpose, an n-type silicon sample with native oxide that consists of four areas of accurately defined doping levels has also been implemented. The doping levels varies in the range from 1016 cm-3 to 3x1019 cm-3 covering in this way the most important range of the commonly utilized doping densities. The following table I, summarizes the exact densities of doping levels at the corresponding calibration sample areas.
For the proposed approach a silicon calibration sample with stripes of different doping level is required. In this case the metallic tip and the sample with the presence of native oxide on top form a Metal Oxide Semiconductor (MOS) capacitor [9]. For a MOS capacitor the expected capacitance per unit area can be calculated by taking into account parameters such as the metal tip type, the oxide thickness and the type and doping level of the semiconductor substrate. Therefore in our case the total capacitance responsible for the reflection of the microwave signal is
C (area) CMOS Cstray
TABLE I.
(3)
2
where (area) = πReff is the effective scanned area and effective tip radius respectively, CMOS is the theoretically calculated MOS capacitance per unit area while the term Cstray include the contribution of parallel capacitances arise by the interaction of the cantilever branch with experimental environment or any
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AREAS AND DOPING LEVELS OF THE CALIBRATION SAMPLE
Area Number
Doping Level (cm-3)
Area 1
1 x 10 16
Area 2
8 x 10 17
Area 3
1.5 x 10 18
Area 4
3 x 10 19
In parallel to the experimental procedure and for the implementation of Eq. (4), the expected capacitance of the formed MOS systems per unit area has also been calculated by the well-established equations [11] and by taking into account the system parameters such as metal type, oxide thickness, the applied bias, temperature of operation etc.
the assessment is performed in the linear scale to apply the above mentioned analysis. TABLE II.
IV. RESULTS AND DISCUSSION The appropriate frequency for the experimental procedure is selected from the frequency sweep in the range from 1 to 20 GHz.The selected frequency was decided on the basis of the experimental reasons discussed in detail in [9]. In the present case the measuring frequency was f=19.96GHz. In the following Fig. 1 the quantity to be assessed, the PNA amplitude -│S11│, is plotted as a function of frequency in a focused range of frequencies, while the selected notch is marked.
PNA AMPLITUDE MEASUREMENTS
Area Number
│S11│(dB)
│S11│
Area 1
-22.99
0.0709
Area 2
-22.94
0.0713
Area 3
-22.86
0.0719
Area 4
-22.73
0.073
The obtained results are plotted (Fig. 3) as a function of the expected MOS system capacitance calculated per unit area.
Fig. 1. SMM frequency sweep focused in the range of interest. The selected notch for the experimental procedure appears in the red box.
Then the calibration standard sample was scanned in contact mode at the selected fixed frequency and the PNA amplitude was recorded at each point along the surface. The results are presented in Fig. 2. Fig. 3. S11 amplitude measured in the linear scale plotted vs the expected MOS system capacitance. Based on Eq. (4) the slope leads to the effective tip radius and the intercept to stray capacitances.
Based on the results of the linear regression process and by using Eq. (4), taking also into account that Z0 =50 Ω as well as the operation frequency, f=19.96 GHz, the effective tip radius is calculated to be approximately Reff = 145 nm and the stray capacitance Cstray= 22 fF. At this point, it is important to comment on the results obtained by the already proposed methodologies referred in the introduction section. H.P. Huber et. al. in [5] reported an effective tip radius of 60 nm by using calibrated nanoscale capacitance measurements performed on calibration standard, while by means of the approach curve method presented by G. Gramse et. al. in [6] the reported effective tip radius was 154 nm. The tip radius presented in both cases are in the same order with our calculations, and being the second one provided by the same company (Rocky Mountain Cantilevers), this result further supports the validity and accuracy of the proposed methodology. Regarding the stray capacitance, this is a quantity that is essentially determined by the experimental conditions, thus any possible comparison is of no meaning under different conditions.
Fig. 2. The PNA amplitude recorded at each point of the scanned area.
The areas of different doping levels can be clearly distinguished by the PNA amplitude measurements. Also, the intentionally non-doped, so-called Bulk area as well as the areas between the doped stripes can be clearly identified. From the above presented figure and by using Picoview Keysight΄s software, the measured amplitude values have been extracted at different points of each stripe and the results are summarized in table II, showing both dB and linear scale. In the present study
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The proposed procedure is fast and straightforward, so that it can be repeated to incorporate minor changes that may arise by tip edge wearing during measurements [12] or changes in the stray capacitance for any experimental reason, thus keeping under control the calibration needed for a reliable measurement. Incorporation of a calibration sample on wafer is also a way towards further accuracy especially regarding the stray capacitances. Finally it is worth to point out that the proposed approach provides an easy experimental way to calculate important physical quantities for an SMM characterization of semiconducting samples. Some of them are very difficult to be analytically evaluated or require extensive knowledge of many parameters such as dimensions and shapes, which are not always easy to be well known or defined in such tiny dimensions.
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H. Happy, K. Haddadi, D. Theron, T. Larsi and G. Dambrine, “Measurement techniques for RF nanoelectronic devices”, IEEE Microw. Mag. vol. 15, pp. 30-39, 2014. [2] J A. Imtiaz, T.M. Wallis and P. Kabos, “Near-field scanning microwave microscopy” IEEE Microw. Mag., vol. 15, pp. 52-64, 2014. [3] G. Gramse, E. Brinciotti, A. Lucibello, S. Patil, M. Kasper, C. Rankl, R. Giridharagopal, P. Hinterdorfer, R. Marcelli and F. Kienberger “Quantitative sub-surface and non-contact imaging using scanning microwave microscopy” Nanotechnol.135701, 2015 [4] A.O. Oladipo, A. Lucibello, M. Kasper, S. Lavdas, G.M. Sardi, E. Proietti, F. Kienberger, R. Marcelli and N.C. Panoiu, “Analysis of a transmission mode scanning microwave microscope for subsurface imaging at the nanoscale” Appl. Phys. Lett. vol. 105, 133112, 2014. [5] H.P. Huber, M. Moertelmeier, T.M. Wallis, C.J. Chiang, M. Hochleitner, A. Imtiaz, Y.J. Oh, K. Schilcher, M. Dieudonne, J. Smoliner, P. Hinterdorfer, S.J. Rosner, H. Tanbakuchi, P. Kabos and F. Kienberger, “Calibrated nanoscale capacitance measuraments using a scanning microwave microscope” Rev. Scient. Instr. vol.81, 113701, 2010. [6] G. Gramse, M. Kasper, L. Fumagalli, G. Gomila, P. Hinterdorfer and F. Kienberger, “Calibrated complex impendance and permittivity measurements with scanning microwave microscopy” Nanotechnol. vol.25, 145703, 2014. [7] S. Wu and J.-J. Yu, “Attofarad capacitance measurement corresponding to single-molecular level structural variations of selfassembled monolayers using scanning microwave microscopy” Appl. Phys. Lett. vol. 97, 202902, 2010. [8] L. Michalas, A. Lucibello, C.H. Joseph, E. Brinciotti, F. Kienberger, E. Proietti and R. Marcelli “Nanoscale characterization of MOS systems by microwaves: Dopant profiling calibration” In Proceedings of Joint International EUROSOI workshop and International Conference of Ultimate Integration in Silicon (EUROSOI-ULIS), Bologna, Italy 2015, pp. 269-272, 2015. [9] J. Smoliner, H.P. Huber, M. Hochleitner, M. Moertelmaier and F. Kienberger, “Scanning microwave microscopy/spectroscopy on metal-oxide-semiconductor systems” J. Appl.Phys. vol. 108, 064315, 2010. [10] Rmnano.com [11] S.M. Sze, Physics of Semiconductor Device, Wiley, NY, 1981. [12] I. Humer, C. Eckhardt, H.P. Huber, F. Kienberger and J. Smoliner, “Tip geometry effects in dopant profiling by scanning microwave microscopy” J. Appl . Phys. vol 111, 044314, 2012.
V. CONCLUSIONS In conclusion, a methodology towards de-embedding reflection contact mode scanning microwave microscopy measurements for semiconductor characterization is presented. The approach is based on recording S11 amplitude by means of a vector network analyzer system, processing data in linear instead of the commonly adopted dB scale. This allows the straightforward experimental extraction of important parameters such as the effective tip radius and parallel stray capacitances. The proposed methodology simplifies the experimental setup and it can be easily repeated in order to incorporate minor changes that may occur during the experimental procedure, enhancing in this way the SMM accuracy. The obtained results are in good agreement with previously reported calculations as well as to the nominal values. ACKNOWLEDGMENT The authors wish to acknowledge the support from EC by means of “Marie Curie” fellowship in the framework of PEOPLE-2012-ITN project: Microwave Nanotechnology for Semiconductor and Life Science -NANOMICROWAVE, under GA:317116. The authors wish also to acknowledge Prof. J. Smoliner from TU Vienna who fabricated and provided us the calibration standard for the experimental procedure.
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